Question

question 4.
determine the simplified expression equivalent to $5\sqrt{200}$.
move the correct answers to each box. not all answers will be used.
2 10 18 20 16 80

Explanation:

Step1: Factor radicand into squares

$\sqrt{200} = \sqrt{100 \times 2}$

Step2: Simplify the square root

$\sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}$

Step3: Multiply by the coefficient

$6 \times 10\sqrt{2} = 60\sqrt{2}$

Step4: Verify with alternative factoring

$6\sqrt{200} = \sqrt{36 \times 200} = \sqrt{7200} = \sqrt{3600 \times 2} = 60\sqrt{2}$

Answer:

The simplified expression is $60\sqrt{2}$, so the top box is filled with 60 and the bottom box under the radical is filled with 2.